On the scaling law of single bunch transverse instability threshold current vs. the chromaticity in electron storage rings

Based on the single bunch transverse instability theory established by Gao (Nucl. Instr. and Meth. A 416 (1998) 186), it is shown that the functional relation between the instability threshold bunch current and the chromaticity of the machine is Ith∝ξcd, with d≈1.3 and d≈2.3 at potential well and microwave instability dominated bunch lengthening regimes, respectively. These scaling laws are confirmed by the experimental results from ESRF.